What Cannot Be Accelerated

Decades, priced

In early August 2026 OpenAI publishes solutions to ten problems in mathematics and theoretical computer science, generated by an internal version of Astra, its announced next model. Each of the ten had stood open for at least a decade: the question whether a group exists that is not sofic, since Gromov introduced the notion in 1999; a conjecture of Connes’s, posed in 1980, now refuted; three problems from the Erdős catalog. Attached are a manuscript of 249 pages and machine-checkable certificates in which no proof step is left open. None of the solutions has been refereed; scrutiny by the field is still to come.

And in the accompanying material stands a number, reported in the tone of a bill of materials: at list prices, the tokens consumed would have cost some two thousand dollars.

The casualness deceives. In that number, decades of search time have been contracted into a line item.

The thesis

The Sprachsubstrat — the language substrate, the material a language model supplies as statistically probable phrasing — contains nothing that was not written. It is statistics over the writing of the species. The certificates of the new proofs show what that means: every step stands within human mathematics and can be checked with tools that humans built. What the species lacked for these solutions was not the capacity. It was the time.

From this, the thesis of this note: the substrate’s contribution resolves entirely into the dimension of time. What it delivers — the perfect application in a minute, the proof after a quarter century of standstill — was reachable; it delivers the reachable sooner. It brings no capacity into the world that was not in it. It shortens the way between the reachable and the reached.

That is a positing, not a measurement. The counter-experiment does not take place; no one leaves the same problems lying for another quarter century to see who solves them without the substrate. But the positing has a floor: a material that only supplies what writing already was can add nothing but the earlier date.

The seal of this project is untouched by the thesis. It counts what actually came from the substrate — how much of the linguistic surface, how much of the ideas — not what would have been reachable in principle. A delivered idea, too, is one that was reachable. What was delivered is the time.

A diagnosis twenty years old

For this finding an apparatus stands ready, and it is twenty years old. In 2005 Hartmut Rosa described acceleration as the signature of modernity: technical acceleration of goal-directed processes, acceleration of social change, acceleration of the pace of life — three dimensions that drive one another, with competition as the wheel that collects every gain in time.

The substrate takes its place in that order. The line of writing technology drawn in Substrate, not Machine — printing press, typewriter, now substrate — reads, with Rosa, as a line of accelerations. The press accelerated the copying of writing, the typewriter the keystroke, the telegraph the transmission. The substrate accelerates the coming-into-being of the phrasing itself. It does not break the line; it is its youngest link and its purest. What is accelerated is no longer the path of writing. It is its production.

So whether this is merely one more iteration of the diagnosis: yes. The finding devalues nothing. A diagnosis confirmed at its youngest link is a diagnosis that holds.

The gain, collected

Rosa also describes why the gain never arrives. Technical acceleration frees time; competition collects it. Where everyone accelerates, it is not the position that shifts but the baseline. The perfect application that costs a minute is an advantage exactly as long as not everyone can write it. After that it is the floor on which everyone stands, and distinguishes nothing.

On the book market this mechanism has already been surveyed — The Flood and Its Bed: the catalog grows many times faster than revenue; what displaces is volume. The sentence from that note, that wording is cheap, receives its more precise version from Rosa. Wording is cheap because it has become cheap in time. What falls toward zero is not the cost of capacity. It is the cost of time.

The rest

Two quantities do not figure in this account. Both are already named in this project’s stock.

Reading. It is slow, and it cannot be delegated — The Witch Trial. A text that came into being in seconds demands the same hours as one that took years. The acceleration ends at the reader. Rosa himself later set a word of his own for what remains withdrawn from it — Resonanz, resonance: that which can neither be accelerated nor placed at disposal.

Standing behind what is said. Whoever stands behind a sentence stands behind it no matter how fast it came to be — Where Calculation Begins. The account of how much substrate went into a work saves no time and costs almost none; it is not a quantity of time. It records how much of the work is owed to the time struck out, and puts a name beneath it.

The substrate delivers time. It delivers no one who stands behind. Rosa’s diagnosis describes completely what the substrate gives; its contribution resolves into the dimension of time. What does not resolve into it is small, slow, and cannot be accelerated. It is this project’s concern.

The derivation of the substrate term: Substrate, not Machine. On the form in which the account is given: Idea.

Self-declaration of this note: W 5 · G 3. Thesis and occasion with the editor — the time dimension and the Rosa question from the editor’s call, the news item from the editor’s reading. Elaboration and linguistic surface substrate-mediated; details checked against the reports; selection, review, and responsibility with the editor.